SOLUTION: solve: sqrt of x+5 + sqrt of x-3 = 4

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Question 255553: solve: sqrt of x+5 + sqrt of x-3 = 4
Found 2 solutions by EMStelley, edjones:
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B5%29+%2B+sqrt%28x-3%29+=+4
When you are solving a problem with two square roots, you always want to start by rearranging the formula to have one square root on each side:
sqrt%28x%2B5%29+=+4+-+sqrt%28x-3%29
Now we square both sides:
%28sqrt%28x%2B5%29%29%5E2+=+%284+-+sqrt%28x-3%29%29%5E2
x%2B5+=+%284-sqrt%28x-3%29%29%284-sqrt%28x-3%29%29
x%2B5+=+16+-+8sqrt%28x-3%29+%2B+x+-+3
Now, we combine like terms and isolate the one remaining square root:
x%2B5+=+x%2B13-8sqrt%28x-3%29
-8+=+-8sqrt%28x-3%29
1+=+sqrt%28x-3%29
And now we square both sides again:
1+=+x-3
x+=+4
The last step is to check our answer:
sqrt%284%2B5%29+%2B+sqrt%284-3%29+=+4
3+%2B+1+=+4
So x=4 is a valid solution.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x+5)+sqrt(x-3)=4
x+5+2sqrt(x+5)sqrt(x-3)+x-3=16 square each side.
2sqrt(x+5)sqrt(x-3)=14-2x
sqrt(x+5)sqrt(x-3)=7-x
(x+5)(x-3)=x^2-14x+49 square each side.
x^2+2x-15=x^2-14x+49
16x-64=0
16x=64
x=4
.
Ed